Syntonic–kleismic equivalence continuum: Difference between revisions

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== Xenial ==

Xenial splits the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. It corresponds to {{nowrap| ''n'' {{=}} 9 }}. Its [[ploidacot]] is zeta-enneacot, and from this it derives its name.

: ''For extensions, see [[Starling temperaments #Xenial]] and [[Sensamagic clan #Xenia]].''

Named by [[User:Xenllium|Xenllium]] in 2026, xenial splits the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. It corresponds to {{nowrap| ''n'' {{=}} 9 }}. Its [[ploidacot]] is zeta-enneacot, and from this it derives its name.

[[Subgroup]]: 2.3.5

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[[Comma list]]: 129140163/125000000

: mapping generators: ~2, ~9/5

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.2802{{c}}, ~10/9 = ~~188~~.~~9887~~{{c}}

* [[WE]]: ~2 = 1200.2802{{c}}, ~9/5 = 1011.2914{{c}}

: [[error map]]: {{val| +0.~~2802,~~ -2.~~0133,~~ +2.~~2783~~ }}

: [[error map]]: {{val| +0.280 -2.013 +2.278 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = ~~188~~.~~9238~~{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.0762{{c}}

: error map: {{val| 0.000 -2.~~2688,~~ +1.~~9824~~ }}

: error map: {{val| 0.000 -2.269 +1.982 }}

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[[Badness]] (Sintel): 10.8

== Parakleismic ~~(5-limit)~~ ==

== Parakleismic ==

: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].''

: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]] and [[Starling temperaments #Paraguay]].''

The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1|3]].

@@ Line 190: / Line 190: @@
 == Xenial ==
-Xenial splits the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. It corresponds to {{nowrap| ''n'' {{=}} 9 }}. Its [[ploidacot]] is zeta-enneacot, and from this it derives its name.
+: ''For extensions, see [[Starling temperaments #Xenial]] and [[Sensamagic clan #Xenia]].''
+Named by [[User:Xenllium|Xenllium]] in 2026, xenial splits the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. It corresponds to {{nowrap| ''n'' {{=}} 9 }}. Its [[ploidacot]] is zeta-enneacot, and from this it derives its name.
 [[Subgroup]]: 2.3.5
@@ Line 196: / Line 198: @@
 [[Comma list]]: 129140163/125000000
-{{Mapping|legend=1| 1 3 5 | 0 -9 -17 }}
+{{Mapping|legend=1| 1 -6 -12 | 0 9 17 }}
+: mapping generators: ~2, ~9/5
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.2802{{c}}, ~10/9 = 188.9887{{c}}
+* [[WE]]: ~2 = 1200.2802{{c}}, ~9/5 = 1011.2914{{c}}
-: [[error map]]: {{val| +0.2802, -2.0133, +2.2783 }}
+: [[error map]]: {{val| +0.280 -2.013 +2.278 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 188.9238{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.0762{{c}}
-: error map: {{val| 0.000 -2.2688, +1.9824 }}
+: error map: {{val| 0.000 -2.269 +1.982 }}
 {{Optimal ET sequence|legend=1| 19, 70, 89, 108, 127 }}
@@ Line 246: / Line 249: @@
 [[Badness]] (Sintel): 10.8
-== Parakleismic (5-limit) ==
+== Parakleismic ==
 {{Main| Parakleismic }}
-: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].''
+: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]] and [[Starling temperaments #Paraguay]].''
 The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1|3]].